Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom

Stability of complex hyperbolic space under curvature-normalized Ricci flow

Using the maximal regularity theory for quasilinear parabolic systems, we prove two stability results of complex hyperbolic space under the curvature-normalized Ricci flow in complex dimensions two and higher. The first result is on a closed manifold. The second result is on a complete noncompact manifold. To prove both results, we fully analyze the structure of the Lichnerowicz Laplacian on complex hyperbolic space. To prove the second result, we also define suitably weighted little H\"{o}lder spaces on a complete noncompact manifold and establish their interpolation properties.Comment: Some typos in version 2 are correcte

Dynamics of Nanometer-Scale Foil Targets Irradiated with Relativistically Intense Laser Pulses

In this letter we report on an experimental study of high harmonic radiation generated in nanometer-scale foil targets irradiated under normal incidence. The experiments constitute the first unambiguous observation of odd-numbered relativistic harmonics generated by the $\vec{v}\times\vec{B}$ component of the Lorentz force verifying a long predicted property of solid target harmonics. Simultaneously the observed harmonic spectra allow in-situ extraction of the target density in an experimental scenario which is of utmost interest for applications such as ion acceleration by the radiation pressure of an ultraintense laser.Comment: 5 pages, 4 figure

Mean curvature flow with triple junctions in higher space dimensions

We consider mean curvature flow of n-dimensional surface clusters. At (n-1)-dimensional triple junctions an angle condition is required which in the symmetric case reduces to the well-known 120 degree angle condition. Using a novel parametrization of evolving surface clusters and a new existence and regularity approach for parabolic equations on surface clusters we show local well-posedness by a contraction argument in parabolic Hoelder spaces.Comment: 31 pages, 2 figure

Energetic beams of negative and neutral hydrogen from intense laser plasma interaction

One of the most striking demonstrations of intermolecular forces is the tension at the surface of liquid n-alkanes. The prediction of surface tension is important in the design of distillation towers, extraction units and tower internals such as bubble caps and trays, since it has a considerable influence on the transfer of mass and energy across interfaces. Surface tension data are needed wherever foaming emulsification, droplet formation or wetting are involved. They are also required in a number of equations for two-phase flow calculations and for determining the flow regime. Petroleum engineers are especially interested in the surface tension in the extraction of crude oil to add surfactants to modify the interfacial properties between crude oil and the geological reservoir to improve production and increase oil yields. In this work, a simple computer program using Arrhenius-type asymptotic exponential function, Vandermoned matrix and Matlab technical computing language, is developed for the estimation of surface tension of paraffin hydrocarbons as a function of molecular weight and temperature. The surface tension is calculated for temperatures in the range of 250 to 440 K and paraffin hydrocarbons molecular weights between 30 and 250. The proposed numerical technique is superior owing to its accuracy and clear numerical background, wherein the relevant coefficients can be retuned quickly if more data become available in the future. Estimations are found to be in excellent agreement with the reliable data in the literature with average absolute deviation being less than 2%

Plasma-Induced Frequency Chirp of Intense Femtosecond Lasers and Its Role in Shaping High-Order Harmonic Spectral Lines

We investigate the self-phase modulation of intense femtosecond laser pulses propagating in an ionizing gas and its effects on collective properties of high-order harmonics generated in the medium. Plasmas produced in the medium are shown to induce a positive frequency chirp on the leading edge of the propagating laser pulse, which subsequently drives high harmonics to become positively chirped. In certain parameter regimes, the plasma-induced positive chirp can help to generate sharply peaked high harmonics, by compensating for the dynamically-induced negative chirp that is caused by the steep intensity profile of intense short laser pulses.Comment: 5 pages, 5 figure

Stable laser-ion acceleration in the light sail regime

We present experimental results on ion acceleration with circularly polarized, ultrahigh contrast laser pulses focused to peak intensities of 5×1019 W cm-2 onto polymer targets of a few 10 nanometer thickness. We observed spatially and energetically separated protons and carbon ions that accumulate to pronounced peaks around 2 MeV containing as much as 6.5% of the laser energy. Based on particle-in-cell simulation, we illustrate that an early separation of heavier carbon ions and lighter protons creates a stable interface that is maintained beyond the end of the radiation pressure dominated acceleration process